On the blow up criterion for the 3D nematic liquid crystal flows involving the second eigenvalue of the deformation tensor

Authors

Ines Ben Omrane, Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P. O.Box 90950, Riyadh 11623, Saudi ArabiaFollow

Author Country (or Countries)

Saudi Arabia

Abstract

In this paper, we study the blow up criterion of the smooth solutions to the three-dimensional incompressible nematic liquid crystal flows in terms of $\lambda _{2}^{+}$ in the multiplier space $\dot{X}_{1}$ and $\nabla d$ in $BMO$. It is shown that the solution $(u,d)$ can be extended beyond $t=T$ if 􏰖 T  􏰇􏰇 λ + ( · , t ) 􏰇􏰇 2 2   2 X ̇ 1 + ∥ ∇ d ( · , t ) ∥ B M O  d t < ∞ . 0 ln(e+∥∇u(·,t)∥X ̇1) ln(e+∥∇d(·,t)∥BMO)

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/170401

Recommended Citation

Ben Omrane, Ines (2023) "On the blow up criterion for the 3D nematic liquid crystal flows involving the second eigenvalue of the deformation tensor," Applied Mathematics & Information Sciences: Vol. 17: Iss. 4, Article 1.
DOI: http://dx.doi.org/10.18576/amis/170401
Available at: https://digitalcommons.aaru.edu.jo/amis/vol17/iss4/1